| Riemann Hypothesis - Chengyan Liu Through an equivalent condition on the Farey series set forth by Franel and Landau, we prove Riemann Hypothesis for the Riemann zeta-function and the Dirichlet L-function. Downloads: 7 | |

| Another Riemann-Farey Computation - Scott B. Guthery Another approach to constructing an upper bound for the Riemann-Farey sum is described. Downloads: 6 | |

| Riemann Zeta Function - Dorin Ghisa Global mapping properties of the Riemann Zeta function are used to investigate its non trivial zeros. Downloads: 14 | |

| A Riemann-Farey Computation - Scott B. Guthery An approach to constructing an upper bound for the Riemann-Farey sum is described. Downloads: 12 | |

| Riemann Musiklexikon 1922 - Hugo Riemann Riemann Musiklexikon 10teA 1922 Musik-Lexikon. Main Author: Riemann, Hugo, 1849-1919. Other Authors: Einstein, Alfred, 1880-1952. Published: Berlin, M. Hesse, 1922. Edition: 10. Aufl. 1469 p. music. = Hathi mdp.39015023343067 Keywords: german; music dictionary Downloads: 280 | |

| Concerning Riemann Hypothesis - Raghunath Acharya We present a quantum mechanical model which establishes the veracity of the Riemann hypothesis that the non-trivial zeros of the Riemann zeta-function lie on the critical line of $\zeta(s)$. Downloads: 5 | |

| The Riemann Hypothesis - Tribikram Pati The Riemann Hypothesis is a conjecture made in 1859 by the great mathematician Riemann that all the complex zeros of the zeta function $\zeta(s)$ lie on the `critical line' ${Rl} s= 1/2$. Our analysis shows that the assumption of the truth of the Riemann Hypothesis leads to a contradiction. We are therefore led to the conclusion that the Riemann Hypothesis is not true. Downloads: 13 | |

| Statistics on Riemann zeros - Ricardo Perez Marco We numerically study the statistical properties of differences of zeros of Riemann zeta function and L-functions predicted by the theory of the e\~ne product. In particular, this provides a simple algorithm that computes any non-real Riemann zeros from very large ones ("self-replicating property of Riemann zeros"). Also the algorithm computes the full sequence of non-real zeros of Riemann zeta function from the sequence of non-real zeros of any Dirichlet L-function ("zeros of L-functions know ab... Downloads: 5 | |

| Riemann compatible tensors - C. A. Mantica Derdzinski and Shen's theorem on the restrictions posed by a Codazzi tensor on the Riemann tensor holds more generally when a Riemann-compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann compatibility is equivalent to the Bianchi identity of the new "Codazzi deviation tensor" with a geometric significance. Examples are given of manifolds with Riemann-compatible tensors, in particular those generated by geodesic mapping... Downloads: 6 | |

| Riemann sums over polytopes - Victor Guillemin We show that the Euler-MacLaurin formula for Riemann sums has an n-dimensional analogue in which intervals on the line get replaced by convex polytopes. Downloads: 5 | |

| Prepotentials and Riemann surfaces - Robert Carroll We organize and review some material from various sources about prepotentials, Riemann surfaces and kernels, WDVV, and the renormalization group, provide some further connections and information, and indicate some directions and problems. Downloads: 4 | |

| On Riemann's mapping theorem - Ashot Vagharshakyan In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case. Downloads: 20 | |

| Computing Riemann Theta Functions - Bernard Deconinck The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation are given. First, a formula is derived allowing the pointwise approximation of Riemann theta functions, with arbitrary, user-specified precision. This formula is used to construct a uniform approximation formula, again with arbitrary precision. Downloads: 3 | |

| Riemann-Christoffel flows - Patricio S. Letelier A geometric flow based in the Riemann-Christoffel curvature tensor that in two dimensions has some common features with the usual Ricci flow is presented. For $n$ dimensional spaces this new flow takes into account all the components of the intrinsic curvature. For four dimensional Lorentzian manifolds it is found that the solutions of the Einstein equations associated to a "detonant" sphere of matter, as well, as a Friedman-Roberson-Walker cosmological model are examples of Riemann-Christoffel ... Downloads: 8 | |

| Yet Another Riemann Hypothesis - Linas Vepstas This short note presents a peculiar generalization of the Riemann hypothesis, as the action of the permutation group on the elements of continued fractions. The problem is difficult to attack through traditional analytic techniques, and thus this note focuses on providing a numerical survey. These results indicate a broad class of previously unexamined functions may obey the Riemann hypothesis in general, and even share the non-trivial zeros in particular. Downloads: 9 | |

| Discrete Riemann Surfaces - Christian Mercat We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincar\'e dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow through to the discrete case, we define the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant argument and series. We present the notion of criticality and its relationship with integrability. Downloads: 6 | |

| Crystallography and Riemann Surfaces - Veit Elser The level set of an elliptic function is a doubly periodic point set in C. To obtain a wider spectrum of point sets, we consider, more generally, a Riemann surface S immersed in C^2 and its sections (``cuts'') by C. We give S a crystallographic isometry in C^2 by defining a fundamental surface element as a conformal map of triangular domains and S as its extension by reflections in the triangle edges... Downloads: 5 | |

| Fuzzy Riemann Surfaces - J. Arnlind We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras. Downloads: 4 | |

| The Riemann Hypothesis - Ilgar Sh. Jabbarov In the paper the well known Riemann Hypothesis is proven. The proof is based on uniform approximation of the zeta function discs of the critical strip placed to the right from the critical line.The basic moment is a use of a new mesure introduced in the infinite dimensional unite cube different from the Haar or product measures Downloads: 7 | |

| Relative Riemann-Zariski spaces - Michael Temkin In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposit... Downloads: 7 | |

| Noncommutative Riemann Surfaces - G. Bertoldi We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1. Following [1], we construct a projective unitary representation of pi_1(Sigma) realized on L^2(H), with H the upper half-plane. As a first step we introduce a suitably gauged sl_2(R) algebra. Then a uniquely determined gauge connection provides the central extension which is a 2-cocycle of the 2nd Hochschild cohomology group. Our construction is the double-scaling limit N\to\infty, k\to-\infty of the representation considere... Downloads: 10 | |

| Noncommutative Riemann Conditions - Eunsang Kim In this paper we study the holomorphic bundles over a noncommutative complex torus. We define a noncommutative abelian variety as a kind of deformation of abelian variety and we show that for a restricted deformation parameter, one can define a noncommutative abelian variety. Also, along the cohomological deformation, we discuss the noncommutative analogue of usual Riemann conditions. This will be done by using the real cohomologies instead of the rational ones. Downloads: 4 | |

| Noncommutative Riemann Surfaces - Joakim Arnlind We introduce C-Algebras of compact Riemann surfaces $\Sigma$ as non-commutative analogues of the Poisson algebra of smooth functions on $\Sigma$. Representations of these algebras give rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets as $N\to\infty$. For a particular class of surfaces, nicely interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the co... Downloads: 19 | |

| Holography and Riemann Surfaces - Kirill Krasnov We study holography for asymptotically AdS spaces with an arbitrary genus compact Riemann surface as the conformal boundary. Such spaces can be constructed from the Euclidean AdS_3 by discrete identifications; the discrete groups one uses are the so-called classical Schottky groups. As we show, the spaces so constructed have an appealing interpretation of ``analytic continuations'' of the known Lorentzian signature black hole solutions; it is one of the motivations for our generalization of the ... Downloads: 5 | |

| Riemann-Roch and Riemann-Hurwitz theorems for global fields - Stella Anevski In this paper, we use counting theorems from the geometry of numbers to extend the Riemann-Roch theorem and the Riemann-Hurwitz formula to global fields of arbitrary characteristic. Downloads: 19 | |

| Riemann flow and Riemann wave via bialternate product Riemannian metric - Constantin Udriste We illustrate the flow or wave character of the metrics and curvatures of evolving manifolds, introducing the Riemann flow and the Riemann wave via the bialternate product Riemannian metric. This kind of evolutions are new and very natural to understand certain flow or wave phenomena in the nature as well as the geometry of evolving manifolds. It possesses many interesting properties from both mathematical and physical point of views... Downloads: 6 | |

| hugo_riemann_armonia_y_modulacion - Hugo Riemann Armonía y modulación de hugo riemann. Escaneado de la edición de editorial Labor. Completo. Keywords: música; riemann; armonía; modulacion Downloads: 58 | |

| On the Riemann-Hilbert Problems - Gia Giorgadze We discuss some topological aspects of the Riemann-Hilbert transmission problem and Riemann-Hilbert monodromy problem on Riemann surfaces. In particular, we describe the construction of a holomorphic vector bundle starting from the given representation of the fundamental group and investigate the local behaviour of connexions on this bundle. We give formulae for the partial indices of the Riemann-Hilbert transmission problem in the three-dimensional case in terms of the correspoding vector bundl... Downloads: 12 | |

| On the Riemann-Lie algebras and Riemann-Poisson Lie groups - Mohamed Boucetta A Riemann-Lie algebra is a Lie algebra $\cal G$ such that its dual ${\cal G}^*$ carries a Riemannian metric compatible (in the sense introduced by th author in C. R. Acad. Paris, t. 333, S\'erie I, (2001) 763-768) with the canonical linear Poisson sructure of ${\cal G}^*$. The notion of Riemann-Lie algebra has its origins in the study, by the author, of Riemann-Poisson manifolds (see Preprint math.DG/0206102 to appear in Differential Geometry and its Applications)... Downloads: 23 | |

| A Riemann sum upper bound in the Riemann-Lebesque theorem - Maurice H. P. M. van Putten The Riemann-Lebesque Theorem is commonly proved in a few strokes using the theory of Lebesque integration. Here, the upper bound $2\pi|c_k(f)|\le S_k(f)-s_k(f)$ for the Fourier coefficients $c_k$ is proved in terms of majoring and minoring Riemann sums $S_k(f)$ and $s_f(k)$, respectively, for Riemann integrable functions $f(x)$. This proof has been used in a course on methods of applied mathematics. Downloads: 8 | |

| Riemann Musiklexikon 10te 1922 - Hugo Riemann Riemann Musiklexikon 10teA 1922 Musik-Lexikon. Main Author: Riemann, Hugo, 1849-1919. Other Authors: Einstein, Alfred, 1880-1952. Published: Berlin, M. Hesse, 1922. Edition: 10. Aufl. 1469 p. music. = Hathi mdp.39015023343067 Keywords: music; dictionary Downloads: 179 | |

| Symmetry of the Riemann Operator - B. Aneva Chaos quantization conditions, which relate the eigenvalues of a Hermitian operator (the Riemann operator) with the non-trivial zeros of the Riemann zeta function are considered, and their geometrical interpretation is discussed. Downloads: 8 | |

| Riemann Musiklexikon 10teA 1922 - Hugo Riemann Riemann Musiklexikon 10teA 1922 Musik-Lexikon. Main Author: Riemann, Hugo, 1849-1919. Other Authors: Einstein, Alfred, 1880-1952. Published: Berlin, M. Hesse, 1922. Edition: 10. Aufl. Physical Description: 1469 p. music. = Hathi mdp.39015023343067 Keywords: music; dictionary Downloads: 108 | |

| Fourier transform in Riemann space - Mark L. Gurari By redefinition of inner product and orthogonality concepts it has been gotten a formula for Fourier transform in Riemann space. Keywords: Riemann space; redefined inner product; orthogonality; Fourier transform Downloads: 72 | |

| Fourier transform in Riemann space - Mark L. Gurari Abstract: By redefinition of inner product and orthogonality concepts it has been gotten a formula for Fourier transform in Riemann space. It is proved, that n-dimensional Riemann space can be considered as two Euclidian n-spaces with one scalar limitation. As a local measure of the Riemann space curvature can be used cosine of angle between these two systems. Keywords: Fourier transform; Riemann space; orthogonality; curvature Downloads: 88 | |

| Symmetries and the Riemann Hypothesis - Lin Weng Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann's zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann hypothesis. Downloads: 5 | |

| Riemann's problem with continuous coefficient - Simonenko, I. B Approximation method of solving Riemann boundary value problem for boundaries between multiple connected regions and their complements Keywords: BOUNDARY VALUE PROBLEMS; CAUCHY PROBLEM; PROBLEM SOLVING; APPROXIMATION; INTEGRAL CALCULUS; LIAPUNOV FUNCTIONS; OPERATORS (MATHEMATICS); RIEMANN MANIFOLD Downloads: 137 | |

| Riemann Musiklexikon 11teA 1929 - Hugo Riemann Riemann Musiklexikon 11teA 1929 Zwei Baende in einem. 2105 S. Including German OCR and alphabetical index Keywords: music dictionary; german Downloads: 2,666 | |

| Riemann Musiklexikon 09teA 1919 - Hugo Riemann Riemann Musiklexikon 09teA 1919 Hugo Riemann's Musik-Lexikon. Main Author: Riemann, Hugo, 1849-1919. Other Authors: Einstein, Alfred, 1880-1952. Published: Berlin : Max Hesses Verlag, 1919. Edition: 9. vom Verfasser noch vollständig umgearb. Aufl. / Note: At head of title: Jubiläums-Ausgabe. Physical Description: xix, 1355 p. : ill. ; 26 cm. = Hathi uc1.b3564129 Keywords: music; dictionary Downloads: 310 | |

| Equivariant Singular Riemann-Roch Theorem - Bin Zhang Equivariant Riemann-Roch theorem for the complex variety under the action of complex linear reductive algebraic group. Downloads: 22 | |

| A Corollary of Riemann Hypothesis - JinHua Fei This paper use the results of the value distribution theory, got a significant conclusion by Riemann hypothesis Downloads: 24 | |

| Existence and computation of Riemann-Stieltjes integrals through Riemann integrals - Rodrigo López Pouso We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we present a new generalization to the well-known formula for continuous integrands and continuously differentiable integrators. Downloads: 4 | |

| Random Construction of Riemann Surfaces - Robert Brooks In this paper, we address the following question: What does a typical compact Riemann surface of large genus look like geometrically? We do so by constructing compact Riemann surfaces from oriented 3-regular graphs. The set for such Riemann surfaces is dense in the space of all compact Riemann surfaces, namely Belyi surfaces. And in this construction we can control the geometry of the compact Riemann surface by the geometry of the graph... Downloads: 3 | |

| An approximate solver for Riemann and Riemann-like Ellipsoidal Configurations - Shangli Ou We introduce a new technique for constructing three-dimensional (3D) models of incompressible Riemann S-type ellipsoids and compressible triaxial configurations that share the same velocity field as that of Riemann S-type ellipsoids. Our incompressible models are exact steady-state configurations; our compressible models represent approximate steady-state equilibrium configurations. Models built from this method can be used to study a variety of relevant astrophysical and geophysical problems. Downloads: 7 | |

| Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces - Miran Cerne Let S be a bordered Riemann surface with genus g and m boundary components. For a smooth family of smooth Jordan curves in the complex plane parametrized by the boundary of S and such that all curves contain 0 in their interior we show that there exists a holomorphic solution of the corresponding Riemann-Hilbert problem with at most 2g+m-1 zeros on S. Downloads: 4 | |

| Higher genus Riemann minimal surfaces - Laurent Hauswirth We construct higher genus Riemann's minimal surfaces properly embedded in the Euclidean space. To do that we glue end by end a Costa-Hoffman-Meeks examples to two halves genus zero Riemann's minimal surfaces. In first we need to perform a deformation of a Costa-Hoffman-Meeks example to prescribe the flux vector along the catenoidal ends. Then we study the mapping property of the Jacobi operator on the half Riemann example as a perturbation analysis of a CMC-Delaunay half cylinder. Downloads: 5 | |

| Riemann Musiklexikon 07teA 1909 - Hugo Riemann Riemann Musiklexikon 07teA 1909 Hugo Riemanns Musik-Lexikon. Main Author: Riemann, Hugo, 1849-1919. Published: Leipzig : M. Hesse, 1909. Edition: 7. vollständig umgearb. Aufl. Note: Issued in 28 pts. Physical Description: xxiii, 1598 p. ; 22 cm. = Hathi uc.b3563636 Keywords: music; dictionary Downloads: 173 | |

| Lagrangians with Riemann Zeta Function - Branko Dragovich We consider construction of some Lagrangians which contain the Riemann zeta function. The starting point in their construction is p-adic string theory. These Lagrangians describe some nonlocal and nonpolynomial scalar field models, where nonlocality is controlled by the operator valued Riemann zeta function. The main motivation for this research is intention to find an effective Lagrangian for adelic scalar strings. Downloads: 4 | |

| The Riemann-Lovelock Curvature Tensor - David Kastor In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \le D Downloads: 5 | |

| Limit Surfaces of Riemann Examples - David Hoffman The family of embedded, singly periodic minimal surfaces of Riemann have as limit-surfaces the helicoid, the catenoid, a single plane, or an infinite set of equally-spaced parallel planes. Downloads: 7 | |